If computing a causal linear regression model of Y = a + bX and the resultant r2 is very near zero, then one would be able to conclude that Y = a + bX is a good forecasting method. 1. None of the alternatives are correct. Y = a + bX is not a good forecasting method. a multiple linear regression model is not a good forecasting method for the data. 2. If a qualitative variable has three categories, how many dummy variables are needed? 3. Which of the following statements is false concerning the hypothesis testing (F-Test) procedure for the overall validity of a regression model? The null hypothesis is that the true slope coefficient is equal to zero. The F-test statistic is used. An level must be selected. The null hypothesis is rejected if the adjusted r2 is above the critical value. 4. Suppose that you believe that a cubic relationship exists between the independent variable (of time) and the dependent variable Y (price of an antique). Which of the following would represent a valid linear regression model? Y = b0 + 3b1 X, where X = time Y = b0 + b1 X, where X = time1/3 (Cube root of time) Y = b0 + 3b1 X, where X = time3 Y = b0 + b1 X, where X = time3 5. A healthcare executive is using regression to predict total revenues. She is deciding whether or not to include both patient length of stay and insurance type in her model. Her first regression model only included patient length of stay. The resulting r2 was .83, with an adjusted r2 of .82 and her level of significance was .003. In the second model, she included both patient length of stay and insurance type. The r2 was .84 and the adjusted r2 was .80 for the second model and the level of significance did not change. Which of the following statements is true? The first model is a better model. None of the alternatives are correct. The adjusted r2 always increases when additional variables are added to the model. The second model is a better model. 6. Johnson's Air, an air conditioning and heating repair firm, conducted a study to determine if the average outside temperature, thickness of the insulation, and age of the heating equipment could be used to predict the electric bill for a home during the winter months in Houston, Texas. The resulting regression equation was: Y = 256.89 - 1.45X1 - 11.26X2 + 6.10X3, where Y = monthly cost, X1 = average temperature, X2 = insulation thickness, and X3 = age of heating equipment If December has an average temperature of 45 degrees and the heater is 2 years old with insulation that is 6 inches thick, what is the forecasted monthly electric bill? $249.57 $136.28 7. With regards to Johnson's Air Study, regression equation Y = 256.89 - 1.45X1 - 11.26X2 + 6.10X3, where Y = monthly cost, X1 = average temperature, X2 = insulation thickness, and X3 = age of heating equipment If January has an average temperature of 40 degrees and the heating equipment is 12 years old with insulation that is 2 inches thick, what is the forecasted monthly electric bill? $112.45 $249.57 8. Shop-Mart Inc Study: Shopmart Inc, a large department store, has collected the following monthly data on lost sales revenue due to theft and the number of security guard hours on duty: Lost Sales Revenue ($000s) 1.0 1.4 1.8 1.9 Total Security Guard hours 1350 1300 1200 1000 Lost Sales Revenue ($000s) 2.0 2.1 2.3 Total Security Guard hours 950 630 600 The least squares regression equation is as follows Lost Sales Revenue (in $000s) = 1.15 + 0.00125 * (Total Security Guard Hours) Lost Sales Revenue (in $000s) = 3.09 - 0.0013 * (Total Security Guard Hours) 9. With regards, to Shop-Mart Inc Study use the regression equation to find the estimated lost sales revenues if the total number of security guard hours is 800. $1700 $1500 $3000 $2052 10. With regards, to Shop-Mart Inc Study the coefficient of determination is -0.7917 0.7917 -0.8898 11. With regards, to Shop-Mart Inc Study the coefficient of correlation is 0.8898 -0.8898 0.7917 12. With regards, to Shop-Mart Inc Study , every 100 hours of additional security guards ____ the lost sales revenue by ____: decreases, $130.59 increases, $130.59 decreases, $1305.9 decreases, $0.0013059 13. With regards, to Shop-Mart Inc Study, if the regression equation is used to predict the lost sales revenue in any given month, the average prediction error can be expected to be 79.17% $2225 $222.5 88.97% 14.A study was done to determine the relationship between GPA and starting salaries for college graduates. The data is shown in the table below: Starting Salary GPA ($) 35,000 37,000 38,000 55,000 60,000 65,000 80,000 2.5 2.7 2.8 3.5 3.6 3.7 3.9 GPA2 (this is the square of GPA) 6.25 7.29 7.84 12.25 12.96 13.69 15.21 15.Using model building to determine the best fit based on highest adjusted R-square, the best model is: None of the alternatives are correct. Y = 227,141.10 - 144385X1 + 27256.08X12, where Y = starting salary, X1 = gpa, and X2 = gpa2. Y = 227,141.10 + 27256.08X12, where Y = starting salary, X2 = gpa2